F(x)=3x^2-2x-6

Solution for F(x)=3x^2-2x-6 equation:

(F)=3F^2-2F-6

We move all terms to the left:

(F)-(3F^2-2F-6)=0

We get rid of parentheses

-3F^2+F+2F+6=0

We add all the numbers together, and all the variables

-3F^2+3F+6=0

a = -3; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-3)·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-3}=\frac{-12}{-6}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-3}=\frac{6}{-6}
=-1
$